Rudiments of Plane Affine Geometry : Mathematical Expositions No. 20 / P. Scherk, R. Lingenberg.

Format:

Book

Author/Creator:

Scherk, P., Author.

Lingenberg, R., Author.

Series:

Mathematical expositions ; Number 20.

Heritage

Language:

English

Subjects (All):

Geometry, Affine.

Genre:

Electronic books.

Physical Description:

1 online resource (114 pages).

Place of Publication:

Toronto : University of Toronto Press, [2020]

Language Note:

In English.

Summary:

In recent decades research into the foundations of geometry has completely transformed the field and created a need for new methods of presenting geometry at the university level. Rudiments of Plane Affine Geometry develops rigorously and clearly one geometric theory accessible to the reader with no previous experience. It reflects the spirit and displays some of the basic ideas of modern geometric axiomatics. The volume is intended for undergraduates with a modest knowledge of algebra and linear algebra and provides a sound introduction to deductive geometry. (Mathematical Expositions No. 20)

Contents:

1. Affine Planes

1.1 The Axioms

1.2 Examples

1.3 A co-ordinate plane

1.4 Finite planes

2. Collineations

2.1Bijections

2.2 Collineations

2.3 Fixed elements

2.4 Homotheties

2.5 Translations

2.6 Dilatations

2.7 Axial Affinities

3. Translation Planes

3.1 Linear Transitivity

3.2 The Configurations of translation planes

3.3 The prime kernel of a translation plane

4. Desarguesiam Planes

4.1 The Dilatation groups D(O)

4.2 The shear theorem

4.3 The linear transitivity of the groups A(a)

5. Pappus Planes

6. Co-Ordinates in Desarguesian Planes

6.1 Co-ordinate planes

6.2 Co-ordinates in desaeguesian planes

6.3 The Fundamental theorem of affine geometry

7. The Projective Closure of an Affine Plane

7.1 Motivation

7.2 The axioms of a projective plane

7.3 The duality principle

7.4 Collineations

7.5 The canonical duality

7.6 Affine restrictions of collineations of projective planes

8. Desarguensian Projective Planes

8.1 Projective and affine desarguesian planes

8.2 The Projective theorem of Desargues

8.3 Projective Pappus Planes.

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 24. Apr 2020)

ISBN:

1-4875-7564-5

OCLC:

1153458256